Rank Spectral Processes and Tests for Serial Dependence

Abstract

Rank analogues of the integrated periodogram spectral process are introduced and used to generate distribution-free tests for independence of a set of random variables. Under simple autoregressive alternatives, the rank spectral process with normal scores yields a test of Kolmogorov-Smirnov type whose local asymptotic efficiency relative to the analogous test based on the integrated periodogram is at least one. Moreover, the same rank test has good local asymptotic efficiency relative to tests based on optimally lagged rank serial correlation coefficients.